Thesis (M.Sc.) National Institute of
Education, Nanyang Technological University

Year

2003

Supervisor

Foong, See Kit

Call
no.

TK5102.9 Lim

Summary

Voltage or current waves
travelling along a transmission line suffer distortion in their waveform,
which may be due to energy dissipation and wave dispersion during the
transmission from one end to the other. The objectives of this project
include the study of the distortions of a square waveform along a coaxial
cable, and the designing of the waveform to be sent such that the waveform
after distortion is the desired square waveform. Only the effects of
dissipation and dispersion on the waveforms were considered in this
project.

Two methods were used in the study of waveform distortion
and the designing. The first method is based on the waveform of sinusoidal
travelling wave having an amplitude which decreases exponentially in the
propagating direction, and a phase velocity that varies with the
frequency. By the use of Fourier series, the effects of dissipation and
dispersion on each component wave were considered and the distorted
waveform was computed. Knowing the line parameters and hence the
propagation characteristics, the Fourier components of the waveform that
should be sent could be constructed from the corresponding components of
the desired square waveform at a predetermined point.

The second method is based on the path
integral solution of the telegrapher's equation which relates the
distorted waveform to the dissipation-free waveform at the same point
along the line. By this relationship, we obtained the distorted waveform
from the dissipation-free square waveform by considering the effect of
dissipation and dispersion on the Fourier components. On the other hand,
by setting the distorted waveform in this relationship as the desired
square waveform, we determined the dissipation-free waveform which was
then used as the designing waveform to be sent.

Experiments to
measure the waveform distortion and tests for square designing waveform
based on the first method were carried out. Results showed that the
waveform designing has improved the distorted waveform, namely the
deviation of distorted waveform from its original waveform has been
reduced. In addition, the observation of distorted waveform has shown
fairly good agreements with the expected distorted waveform, in terms of
the decreasing amplitude with distance travelled and the speed of
propagation. Results showed that the method of designing was able to
overcome the waveform distortion with an approximate capability of
2/3.